Duct or recirculate?
When you install a rangehood, it can be either ducted to the outside or set up to recirculate the air within the kitchen. It is now illegal to duct into the ceiling cavity, because the build-up of grease can be a fire hazard and moisture can cause condensation and rot. With the recirculation option, most of the grease and smells should be trapped by a special carbon filter. Moist air will still contribute to condensation problems and some smells may escape.
However, with external ducting, the process of removing a lot of hot air quickly does mean the room gets a little cooler. If you're used to having the oven help heat your kitchen or kitchen/living area, you may need to think about an extra heating source.
If you're in an apartment, recirculating the air may be the only option, but it should only be considered if you can't duct to the outside.
Tip: When installing a rangehood it’s best to use rigid ducting. Flexible ducting has ridges which can trap air and impede performance.